Interplay between Covalent and Physical Interactions within

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Biomacromolecules 2009, 10, 1090–1099

Interplay between Covalent and Physical Interactions within Environment Sensitive Hydrogels Kyung Jae Jeong† and Alyssa Panitch*,‡ Weldon School of Biomedical Engineering and School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47906 Received November 5, 2008; Revised Manuscript Received January 29, 2009

A systematic study is carried out to understand how physical and covalent crosslinks affect the mechanical properties of an eight-arm poly(ethyleneglycol)-based hydrogel. Heparin and heparin-binding peptide are used as a physical crosslinker, and an enzymatically cleavable peptide with a cysteine on each end serves as a covalent crosslinker. While physical crosslinks alone do not induce gelation due to the low binding affinity between heparin and heparinbinding peptide, the addition of covalent crosslinks leads to gel formation. Strikingly, the addition of the covalent crosslinks not only leads to gel formation, but also enhances the contribution from the physical crosslinks to the overall shear moduli, which are negligible in the absence of covalent crosslinks. The gels, which contain both covalent and physical crosslinks, are able to reversibly respond to external stimuli such as temperature and oscillatory shear unlike the purely covalent gel in which the moduli remain largely insensitive to such stimuli. Two explanations are provided for this striking phenomenon. First, the addition of covalent crosslinks increased the stress relaxation time of the gel enabling the physical interactions to contribute to the moduli. This is contrasted to the case of physically crosslinked material, which relaxes the stress too quickly, preventing the physical interactions from contributing to the low frequency moduli. Second, it is believed that the physical interactions within the covalent network were further enhanced by “macromolecular confinement”, which favors the formation of compact conformational structures in the confined space. Quartz crystal microbalance (QCM) was used to measure the dissociation constant (Kd) within the hydrogel and to demonstrate that the binding between heparin and heparinbinding peptide is stronger within the gel compared to that within the solution phase. Because extracellular matrix (ECM) contains both covalent and physical interactions between its constituents, and the mechanical properties of the ECM are important factors to control cell functions, the findings of this research may have important implications in various fields of tissue engineering and cell biology.

I. Introduction Extracelluar matrix (ECM) is made of various proteins, proteoglycans, and glycosaminoglycans and is responsible for numerous cellular functions such as cell adhesion and migration, cell proliferation and cell differentiation.1-9 It not only provides anchors for cells to adhere to but also provides biological signals, both chemical and physical, and functions as a reservoir for growth factors and cytokines. Recent studies have revealed the importance of the mechanical properties of ECM in controlling cellular behavior in addition to its chemical influence.10-17 The mechanical properties of the soft tissue ECM may originate from the identity of and the interactions between the constituent macromolecules, which are bonded through various forms of covalent and physical bonds. The covalent bonds maintain the integrity of the structure of the macromolecules and their networks, whereas the physical bonds both contribute to matrix integrity and also provide means for the system to dynamically respond to the external stimuli such as temperature, pH, and mechanical loading. Recent years have witnessed rapid advancement of tissue engineering inspired by biomimetic materials that resemble the natural ECM. Polymer-based biomaterials have been used as scaffolds for tissue growth,18,19 as controlled drug release vehicles,20 and as a model system for the systematic study of * To whom correspondence should be addressed. E-mail: apanitch@ purdue.edu. † School of Chemical Engineering. ‡ Weldon School of Biomedical Engineering.

cells and tissues.21 In general, these materials are crosslinked by purely covalent bonds,22-25 purely physical bonds,26-32 or a mixture of both.33-38 In our previous studies, a novel hydrogel-like material, composed of multiarm poly(ethylene glycol) (PEG) crosslinked by the physical interactions between a polysaccharide, heparin, and heparin-binding peptides (HBPs) was described.31 In this material, HBPs were conjugated to PEG, and PEG-co-HBP molecules were crosslinked in the presence of heparin. This gellike material exhibited a dynamic response to external stimuli such as oscillatory shear and temperature under dynamic rheological testing due to the presence of physical bonds between heparin and HBPs. Because it is known that various growth factors such as fibroblast growth factor (FGF), vascular endothelial growth factor (VEGF), and bone morphogenetic promoter (BMP) bind to heparin,39 this material can be used as a drug delivery vehicle with the controlled drug release rate depending on the affinity between heparin and the growth factors. This work was followed by the development of a hybrid system in which the covalent crosslinkers were added to the previous physically crosslinked material.37,38 This material exhibited the behavior of purely covalent polymer network in low frequencies and high temperatures and the contribution of the physical interactions gradually increased as the frequencies increased or the temperatures decreased. This novel class of biomaterials has potential to be used not only as a drug delivery system but also as a model system through which the roles of

10.1021/bm801270k CCC: $40.75  2009 American Chemical Society Published on Web 03/23/2009

Interactions within Environment Sensitive Hydrogels

covalent and physical bonds in the ECM and how they determine the overall mechanical properties of the ECM can be deduced. How different crosslinking methods affect the mechanical properties of the hydrogel has been studied by several groups.37,40,41 However, it has been generally regarded that the contributions from the covalent and physical crosslinks to the mechanical properties of the gel are independent, meaning that the mechanical properties of a hydrogel would be the linear sum of covalent and physical gels. The possibility that covalent and physical interactions might affect the nature of one another within the hydrogel network has been largely ignored. This article presents a systematic study, using dynamic rheological testing, designed to investigate how the various ratios of the physical and covalent crosslinks determine the mechanical properties of the hydrogel. Surprisingly, the results show that the addition of covalent crosslinks to the physically crosslinked hydrogel-like material enhanced not only the overall strength of the material but also the contribution of the physical bonds to the overall mechanical properties by several orders of magnitude. We attribute this phenomenon to the increased stress relaxation time of the polymer network due to the covalent crosslinking. We also hypothesized that macromolecular confinement effect is partially responsible for this intriguing phenomenon. To confirm this hypothesis, dissociation constant (Kd) between heparin and peptides was measured within the hydrogel using quartz crystal microbalance (QCM) and was compared to the Kd measured in the solution phase. We discuss the potential implications of these findings in tissue engineering and cell biology.

II. Materials and Methods Materials. Eight-arm poly(ethylene glycol) (PEG; MW 20000) was purchased from Nektar (Huntsville, AL), divinyl sulfone, 1,2ethanedithiol, and N-methylmorpholine (NMM) were purchased from Alfa Aesar (Ward Hill, MA), magnesium sulfate, hydrogen peroxide (H2O2), acetic anhydride, diethyl ether, acetonitrile, dichloromethane (DCM), dimethylformamide (DMF), and activated charcoal were purchased from Mallinckrodt (Hazelwood, MO), sodium hydride (NaH), anhydrous dichloromethane, sulfuric acid (H2SO4), dithiothreitol (DTT), high molecular weight heparin (from porcine intestinal mucosa), 6-mercapto-1-hexanol (MCH), and celite were purchased from Sigma Aldrich (St. Louis, MO), anisole, triisopropylsilane from TCI (Portland, OR), and trifluoroacetic acid (TFA) were purchased from Acros Organics (Morris Plains, NJ), and all amino acids, O-benzotriazoleN,N,N′,N′-tetramethyl-uronium-hexafluoro-phosphate (HBTU), and rink resin were purchased from Anaspec (San Jose, CA). Conjugation of Divinyl Sulfone to Multiarm PEG. Conjugation of divinyl sulfone to multiarm PEG was done following a slight modification of the work reported by Rizzi et al.42 A total of 10 mL of DCM for every 200 mg PEG, 5 times molar excess of NaH over hydroxyl groups in PEG, and 100 times molar excess of divinyl sulfone over hydroxyl groups in PEG were used. Briefly, divinyl sulfone and NaH were dissolved in anhydrous DCM in a round-bottom flask. To this, PEG dissolved in anhydrous DCM was added dropwise. This mixture was stirred under nitrogen at room temperature for 3 days. The reaction was stopped by adding a molar equivalent of acetic acid to NaH. The product was filtered through the filter paper and the solvent was evaporated to a final volume of 30 mL. After precipitating the product with ethyl ether and recovering it by filtration, it was washed with two volumes of ether and collected by passing 200 mL of DCM through the filter. It was extracted with 200 mL of NaCl-saturated water and treated with activated carbon for 30 min. The activated carbon was removed by filtration through a bed of celite. The product was dried by adding magnesium sulfate, followed by filtration, and the solvent was evaporated to a final volume of 20 mL. Finally, it was

Biomacromolecules, Vol. 10, No. 5, 2009

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Table 1. Sample I.D. Based on the Composition of the Hydrogel sample I.D.

covalent crosslinker per PEGa

physical crosslinker per PEG

4C-0P 4C-2P 4C-4P 2C-4P 0C-4P

2 2 2 1 0

0 2 4 4 4

a

Covalent crosslinker crosslinks two PEG molecules.

precipitated by ethyl ether and washed with ether to remove all residual divinyl sulfone. After redispersing the product in water, it was frozen in -80 °C, lyophilized, and stored at -20 °C until use. The successful synthesis was confirmed by three hydrogen peaks of vinyl sulfone (VS) group in NMR spectrum at δ 6.0-6.1, 6.3-6.4, and 6.8-6.9 ppm, and greater than seven of the eight PEG arms were functionalized with vinyl sulfone as determined by NMR. A fluoraldehyde assay confirmed that all eight arms of the PEG-VS react via Michael-type addition of primary amines to vinyl sulfone groups (data not shown). Synthesis of Peptide. Conventional solid phase Fmoc chemistry was used to synthesize the peptides. The sequences of covalent and physical crosslinker peptides were GCRGDSDPQGIGQGC (MW 1462) and RVFKRYKRWLRVFKRYKRWLRGC (MW 2818), respectively. The amino acids dissolved in DMF were added to the growing chain of peptide on rink resin under nitrogen. Prior to the addition of amino acids, the Fmoc protecting group at the end of the growing peptide chain was removed by HBTU. At the end of the synthesis, the peptide was cleaved by the mixture of TFA, water, ethanedithiol, anisol, and triisopropylsilane (90, 2.5, 2.5, 2.5, and 2.5% v/v concentration, respectively). After precipitating the final product with ethyl ether, the peptide was dissolved in water and lyophilized. The peptide with the ¨ KTA FPLC system desired amino acid sequence was purified using an A (GE Healthcare, Waukesha, WI) with a reverse phase C18 column (Grace-Vydak, Deerfield, IL) in 0.1% TFA water with increasing concentration of acetonitrile. Because all peptides used contained free thiols, the final products were treated with DTT prior to purification in order to reduce any disulfide bonds between peptides. MALDI-TOF was used to verify the molecular weight of the final product. The peptides were lyophilized and kept at -20 °C until use. Conjugation of PEG-VS with Peptide. PEG-VS was conjugated to peptide through Michael-type addition between the free thiols of cysteine residue on the peptide and the vinyl sulfone group on PEGVS. Typically, 5 mg PEG-VS was mixed with the peptide at the desired molar excess (either 0, 2, or 4 times molar excess) in 150 mM phosphate buffer (PB) at pH 7.5. This buffer was chosen to enhance the efficiency of the conjugation chemistry because Michael-type addition is known to be more efficient in higher buffer concentrations.43 The final concentration of the mixture was 10% (w/v). The mixture was kept in the dark for 4 h. Based on the results of previous experiments on rate and completion of Michael addition in the system, it was assumed that most of the peptides were conjugated to PEG and no further purification was needed.38 Rheology. All rheological measurements were made using an ARG2 (TA Instrument, New Castle, DE) with the conical geometry (1 cm in diameter and 1° cone angle). PEG-VS conjugated with the desired amount of HBP was mixed with heparin and the covalent crosslinker. Various combinations of HBP and covalent crosslinker were tested by rheometry as listed in Table 1. For 4C-0P, no heparin was added because incorporation of heparin to the covalently crosslinked gels in the absence of peptide did not affect G′ (unpublished observations). The molar ratio of peptide to heparin was about 14.5. The mixture with the total volume of 50 µL was placed on the stage. Mineral oil was added around the sample and the geometry to avoid the evaporation of water. For each sample, the following series of measurements were performed: the gelation by covalent crosslinker was monitored for 3 h at 10 rad/s. Then, the frequency sweep was done between 0.1 and 100 rad/s at 25 °C followed by the temperature sweep between 5 and 45

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°C at 10 rad/s. All measurements were performed in the previously determined linear viscoelastic regime. AFM Single Molecule Force Measurement. AFM single molecule force measurements were performed to calculate the lifetime of the binding between heparin and HBP. For AFM force measurements, HBPs were immobilized on both the glass coverslip and AFM cantilever. For this, 1 mM R-maleimide-ω-(N-hydroxysuccimide)-PEG (MAL-PEG-NHS, MW 3500, Jenkem U.S.A., Allen, TX), dissolved in PBS, was added to the amino-terminated glass coverslip and AFM cantilever (Novascan, Ames, IA) for 2 h. After rinsing both the coverslip and the cantilever with deionized water, both surfaces were treated for 4 h with 1 mM HBP dissolved in 150 mM PB. AFM force measurements were performed using Nanoscope IV from Veeco (Plainview, NY). First, 150 mM PB solution containing no heparin was added to the liquid cell as a control experiment. Then, the force measurements were done after replacing the buffer with 1 µM heparin in 150 mM PB. The force measurements were done with the approach velocity at 200 nm/s and the retraction velocities at 200, 1000, and 2000 nm/s. The spring constant of the cantilever was 0.07 nN/nm determined by the thermal analysis.44 For each retraction velocity, the most probable rupture force was determined by fitting the force histogram with a Gaussian function. Following the method described by Strunz et al.,45 the lifetime of the binding was found by fitting the retraction velocity versus the most probable rupture force data with the following equation

F)

(

kBT ucx ln x kBTkoff

)

(1)

where F, kB, T, x, u, c, and koff represent the most probable rupture force, Boltzman constant, temperature, the distance between the energy minimum to the energy barrier during the rupture event, retraction velocity, elasticity of the binding, and the off-rate, respectively. QCM. QCM (Stanford Research, Sunnyvale, CA) was used to determine the dissociation constant of the binding between heparin and HBP within the gel. The gold-coated quartz crystal with a 1 cm diameter was cleaned in piranha solution (H2SO4 70% and H2O2 30%) and rinsed with water thoroughly. After drying the surface under nitrogen, 1 mM crosslinker peptide in 150 mM PB was added to the crystal surface for 4 h. Then, 4C-4P sample (Table 1) without heparin was spread onto the crystal using the spin coater at 2000 rpm for 1 min. After 3 h, the crystal was mounted on the QCM and the system was equilibrated in the buffer until the frequency response (14.9 MHz) became constant. Heparin at various concentrations (0, 6.25, 12.5, 25, 50, 100 µM) was added to the chamber until the frequency shift reached saturation for each concentration. The final frequency shifts (∆f) were plotted as a function of heparin concentration, [H], and fitted with the following equation to determine the dissociation constant.

-∆f )

B[H] Kd + [H]

(2)

B is a hypothetical maximum ∆f at the infinite [H]. To compare this result with the dissociation constant between the peptide and the heparin in the gel-free state, 1 mM HBP was added to the gold-coated crystal surface for 4 h, followed by the addition of 1 mM 6-mercapto-1-hexanol (MCH) for 1 h, and the frequency shift was monitored as a function of heparin concentration.

III. Results Table 1 shows the various combinations of physical and covalent crosslinking present in the hydrogel variants with the sample I.D. for each combination. Physical crosslinks are formed between heparin and the heparin-binding peptide (HBP) that is

Figure 1. G′ (black) and G′′ (gray) of 4C-0P as a function of time. Oscillation frequency and stress were 10 rad/s and 0.5 Pa, respectively.

conjugated to PEG arms through Michael-type addition between the vinylsulfone group on PEG and a free thiol on the cysteine residue of the HBP. Vinyl sulfone functionality was chosen for conjugation to peptides as under physological conditions, the chemistry is selective for thiols over amines allowing conjugation specifically to cysteines and preserving amines for interactions with heparin.46 In addition, the vinyl sulfone is more stable than maleimide under aqueous conditions. The physical crosslink is reversible and transient. The binding between heparin and peptide will constantly form and break and the average number of crosslinks within the hydrogel is determined by the dissociation constant (Kd). Covalent crosslinker is a peptide that contains, in addition to two cysteine residues, an RGD cell adhesion site, and an enzymatically cleavable site whose presence would facilitate cell adhesion and enzyme-dependent cell migration studies in the future. The covalent crosslinks formed between the cysteine thiols and the vinyl sulfone groups are irreversible under the given experimental conditions. To understand how the physical and covalent bonds control the mechanical properties of the hydrogel, two different sets of experiments were performed. In the first set, the number of physical crosslinks varied while the number of covalent crosslinks remained fixed, and in the second set, the number of covalent crosslinks varied while the number of physical bonds was fixed. Figure 1 shows the kinetics of gelation when four arms of the PEG are covalently crosslinked (4C-0P). The gelation time, which is generally defined as the time for the storage modulus (G′, black) to surpass the loss modulus (G′′, gray), occurred within 5 min, and the whole reaction reached saturation in about 3 h. After gelation, the mechanical properties of the gel were dominated by G′, while G′′ remained about an order of magnitude smaller than G′, which means the viscoelastic properties of the gel were dominated by elasticity. Therefore, throughout this paper, only G′ is presented for all rheological experiments. Figure 2 shows how physical bonds affect the mechanical properties of the gel when the number of covalent crosslinks is kept constant. 4C-0P is crosslinked solely by covalent crosslinks. Theoretically, four of the eight available arms on the eight-arm PEG were covalently crosslinked while the remaining four arms of the PEG remained free. G′ of this hydrogel was insensitive to the frequency changes (Figure 2a), which is characteristic of



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Figure 2. Frequency (a) and temperature (b) sweeps for 4C-0P (square), 4C-2P (triangle), and 4C-4P (diamond). The oscillation stress was 0.5 Pa. For the temperature sweep, the angular frequency was kept at 10 rad/s.

covalent gels. However, G′ of 4C-0P slightly increased as the temperature was raised from 4 to 45 °C (Figure 2b). This increase may be due to the entropic spring effect, which predicts that the polymer chains become stiffer at higher temperatures because of the higher entropic penalty. When physical crosslinks were added (both 4C-2P and 4C-4P), the storage moduli of the hydrogels increased with increasing frequency (Figure 2a) as is characteristic of physically crosslinked polymer networks. In addition, as the number of physical crosslinks increased, the hydrogel became more responsive to the frequency changes since there were more physical bonds to form and break. For example, the storage modulus of 4C-2P increased by 861 Pa over this frequency change, while it increased by 1953 Pa for 4C-4P. In the temperature sweep, Gs of both 4C-2P and 4C-4P decreased significantly with increased temperature (Figure 2b). The decrease in G′ is due to a decrease, at any given time, in the average number of physical bonds between heparin and peptide as the temperature was raised. However, due to the presence of covalent crosslinks, G′ did not reach zero even after all physical bonds had melted, meaning that covalent crosslinks mechanically stabilized the gel. Figure 3 shows how the covalent bonds affect the viscoelastic properties of the gel when the number of physical crosslinks is kept constant. 0C-4P is crosslinked purely by physical binding. On average, four arms of the eight-arm PEG were modified with HBP, which binds to heparin. There are two fundamental differences in the physical crosslinks compared to the covalent crosslinks. Although maximally four arms of the eight-arm PEG can be modified with heparin-binding peptides, not all of them would participate in crosslinking adjacent PEG molecules

Figure 3. Frequency (a) and temperature (b) sweeps on 0C-4P (square), 2C-4P (triangle), and 4C-4P (diamond). (c) The linear scale plot of (b). Oscillation stress was 0.5 Pa. For the temperature sweep, the angular frequency was kept at 10 rad/s.

simultaneously. In addition, the crosslinks are transient due to the thermal motion of the molecules. The gelation was not detected for 0C-4P because the binding between heparin and peptide was not sufficiently strong. When two arms of PEG-VS were covalently crosslinked, in addition to four physical crosslinks (2C-4P), the viscoelastic properties of the material changed dramatically. First, it became a much stiffer gel-like material than 0C-4P in general. Not only did it become stiffer, it also became more responsive to the external stimuli, which means the contribution of the physical crosslinks to the overall mechanical properties of the gel was greatly enhanced. Utilizing the temperature sweep data (Figure 3b), the contribution of each covalent crosslink to G′ is estimated to be about 42.8 Pa based on G′ at 45 °C, a temperature at which the contribution of the physical bonds should be negligible. However, as the temperature was lowered, G′ increased significantly (1712 ( 232 Pa at 4 °C). Because the covalent

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the contribution from one heparin-peptide interaction to G′ increased as the number of covalent crosslinks increased (Figure 4b).

IV. Discussion

Figure 4. Summary of the interplay between covalent and physical crosslinkers within the hydrogel. (a) Contribution from one physical crosslinker to G′ change in the temperature sweep as a function of the number of physical crosslinkers. (b) Contribution from one physical crosslinker to G′ change in the temperature sweep as a function of the number of covalent crosslinkers.

crosslinks do not cause the increase of G′ with the temperature, and in fact may slightly decrease G′ due to the entropic spring effect, the physical crosslinks should be responsible for this significant increase in G′. This phenomenon becomes more evident in the linear plot (Figure 3c). This is a striking difference compared to 0C-4P to which the same number of physical crosslinkers was added, with the only difference being two additional PEG arms were covalently crosslinked in the 2C-4P materials. When two additional arms of PEG were covalently crosslinked (4C-4P), the stiffness of the gel further increased. Again, the increase in covalent crosslinks resulted in a higher sensitivity to frequency and temperature changes (4C-CP > 2C4P > 0C-4P). For example, in the case of 4C-4P, G′ varied over 2622 Pa during the same temperature sweep where G′ varied ∼1700 Pa for 2C-4P. These results clearly show that the mechanical properties of the hydrogel, which contains both physical and covalent crosslinks, are not a linear sum of those of purely physical crosslinks and of purely covalent crosslinks. Rather, the addition of covalent crosslinks affects the nature of the physical crosslinks in a way that amplifies the contribution of physical bonds to the overall strength of the hydrogel and the sensitivity to the external stimuli. Figure 4 summarizes the effects of covalent crosslinks on the physical binding between heparin and peptide within the hydrogel. In this figure, the difference between G′ at 45 °C and G′ at 4 °C was divided by the number of physical crosslinker peptides added to the hydrogel. This can be interpreted as the contribution from one heparin-peptide interaction to G′ per PEG. When the number of covalent crosslinks was fixed, the contribution from one physical crosslink to G′ was almost constant, so that the changes in G′ over the temperature sweep were proportional to the number of physical crosslinks added (Figure 4a). However, when the number of physical crosslinks was fixed and the number of covalent crosslinks was varied,

The main finding of this article is that the contribution of the physical crosslinks to the shear moduli of the material increased significantly as more covalent crosslinks were added. The average number of physical crosslinks is responsible for the dynamic response of the material to the frequency changes of shear or the temperature of the system. Then, why, for the same number of heparin and HBPs, does one system (4C-4P) respond to such stimuli significantly, while the other (0C-4P) does not? One possibility is that, due to the inherent difference in the molecular environment, the average number of physical crosslinks was higher in 4C-4P than in 0C-4P even though the same number of heparin and HBPs were initially present. The other possibility is that, even with the same number of physical crosslinks, each system relaxes the stress in fundamentally different ways, resulting in the drastic differences in response to frequency and temperature changes. The latter possibility will be addressed first. When stress is applied to physically crosslinked polymers, they relax the stress in different modes with distinct relaxation times. The relaxation modes relevant to the physically crosslinked systems are the Zimm, Rouse, and cluster relaxation modes.47 Here, “cluster” stands for a finite group of PEG monomers connected to each other through physical crosslinkers. Among these, Zimm and Rouse relaxation times, which correspond to the relaxation times of chain segments and single chains, respectively, are much shorter (2 elastically active physical crosslinks between chains at any given time increases as temperature decreases and is manifested in G′. Finally, the hybrid gel (4C4P) is already an infinite polymer network due to the presence of covalent crosslinks regardless of temperature or oscillation frequency. Therefore, the increased number of physical bonds within the hydrogel caused by the temperature drop increases the number of elastically effective polymer chains, which was manifested as significant increases in G′ at low temperatures. Entropic spring effect, which slightly reduces G′ in low temperatures, is still in effect even in hybrid gels, but the



increase in the number of elastically active chains in lower temperatures dominates the rheological properties of the gels. There is another fundamental difference in the nature of the physical binding between the purely physically crosslinked material (0C-4P) and the hybrid gel (2C-4P and 4C-4P). The binding between heparin and peptide in the purely physically crosslinked material takes place in an “open” space, whereas the binding in the hybrid materials occurs in a “confined” space defined by the mesh size of the covalent network (Figure 5). It is known that a confined space with the characteristic length close to that of the macromolecules affects the kinetics and the equilibria of the macromolecular binding, favoring the formation of the products with more compact conformations.48,49 The importance of “macromolecular confinement”, as it is termed in biology, has begun to be understood as many of the cellular and physiological processes occur in crowded and confined environments. This suggests that it was likely that 4C-4P had a higher number of heparin-peptide bonds at equilibrium than 0C4P due to the confinement effect even though both systems contained the same number of heparin and peptide molecules. To prove that the confinement effect affected the equilibrium of the heparin-peptide binding within the hydrogel, the dissociation constant (Kd) between heparin and peptide was determined both in and out of the hydrogel. For this purpose, a quartz crystal microbalance (QCM) was used. According to Sauerbrey equation, in QCM, the mass of molecules bound to the crystal surface is linearly proportional to the decrease in the frequency of the crystal vibration.

-∆f )

2∆mf 20 A(Fqµq)1/2

(3)

Here ∆f, f0, n, ∆m, A, Fq, and µq stand for frequency change, resonant frequency, harmonic number, mass change, piezoelectrically active crystal area, density of quartz, and shear modulus of quartz for AT-cut crystal, respectively. By forming a thin film of hydrogel (4C-4P) without heparin and by monitoring the amount of heparin bound to the hydrogel film as a function of heparin concentration in the chamber, one can estimate the dissociation constant. This method has been used to determine the binding constant of the molecularly imprinted polymers for various target molecules.50 For this, 4C4P but without heparin was spin-coated on the gold coated quartz crystal surface which was pretreated with the covalent crosslinker. Figure 8 shows the frequency changes as a function of heparin concentrations. Dissociation constants were obtained by fitting the frequency shift versus heparin concentration data with eq 1. Kd between individual peptide and heparin molecules was determined in the same way except that the heparin-binding peptide was directly immobilized on the gold-coated crystal surface through the cysteine residue of the peptide. Kds determined by this method are shown in Figure 8. We do not have a clear explanation on why there was more frequency change (more heparin binding) without the hydrogel. One possible explanation is that only a few molecular layers of PEGpeptide were accessible to heparin while most of the heparin binding sites were buried inside the hydrogel. Clearly, on the surface, there are more binding sites with peptide alone because in the hydrogel, peptides are diluted with PEG macromolecules. However, the Kd values show that the binding between heparin and peptide is greatly enhanced if the peptide is embedded

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Figure 8. Estimating Kd of heparin-peptide binding on the surface (a) and within the hydrogel (b). These plots were fitted to eq 2 to estimate Kds.

within the covalent network, which we attribute to the macromolecular confinement effect. The macromolecular confinement effect has been demonstrated in various biological interactions. For example, Cisse et al. have shown that the binding between RecA and DNA is enhanced by 2 orders of magnitude within the confined space of lipid vesicles.51 And Moorthy et al. have proven that the affinity between protein A and IgG increased considerably inside the hydrogel.52 In this paper, we demonstrated that this effect can also influence the mechanical properties of the polymer if one of the binding molecules is connected to the covalent network and can participate in bearing the mechanical loads. As additional covalent crosslinks are added, the binding between heparin and peptide takes place in more confined spaces, driving the equilibrium more toward the bound state and increasing the contribution from the physical interactions to the mechanical properties of the gel. This explains the trend shown in Figure 4b, where the physical interactions contribute more to the shear moduli as additional covalent crosslinks are added. The described phenomena are consistent with that seen by Shen et al.53 They found that in a protein-based hydrogel, reliant purely on physical crosslinks, the time scale of the protein association, which was controlled by pH, and the stress relaxation time are related: as protein association time increases, the stress relaxation time also increases. Their results suggest that by changing the affinity between the proteins, one can tailor the dynamic mechanical properties of the hydrogel. This is consistent with the results shown here in two ways. First, as temperature was lowered, the affinity between heparin and HBPs increased resulting in an increase in G′ (Figures 2b and 3b), which most likely coincided with the increase in stress relaxation time. Second, as covalent crosslinkers are added, due to molecular confinement, the apparent affinity between the HBP and heparin increases, thus increasing the mechanical properties of the materials.

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In simple mathematical terms, the above arguments can be summarized as follows. The storage modulus for physical gel can be written as phy G′ ) veff (ω, T)kBT

(4)

This simply means that each elastically effective chain contributes as much as kBT to G′. For the gel containing both covalent and physical crosslinks, it can be written as phy G′ ) (νcov 0 + νeff (ω, T))kBT

(5)

Here, νphy eff stands for the number of elastically effectiVe polymer chains formed by physical interactions at a given frequency and temperature, ν0cov stands for the number of elastically effective polymer chains formed by covalent interactions, and kBT stands for the thermal energy. ν0cov is considered a constant, whereas phy is a function of frequency and temperature, which can be νeff written as phy ) νphy(ω, T) νeff

e∆G/kBT 1 + e∆G/kBT

(6)

νphy is the maximum possible number of elastically effective chains at a given frequency and temperature and ∆G is the free energy of binding. This equation, derived by Tanaka and Edwards,54 states that out of all potential chains that can contribute to shear moduli at a given frequency and temperature, only the portion of (e∆G/kBT)/(1 + e∆G/kBT) would be elastically effective. Combining all these, eqs 4 and 5 can be rewritten as

G′ ) νphy(ω, T)

(

e∆G/kBT kBT 1 + e∆G/kBT

phy G′ ) νcov 0 + ν (ω, T)

(7)

)

e∆G/kBT kBT 1 + e∆G/kBT

(8)

According to the argument based on the stress relaxation time, ν0cov and νphy are not independent, but an increase of ν0cov causes an increase of the relaxation times of the polymer clusters, which in effect increases the number of potentially elastically effective chains, νphy, resulting in an increase of the contribution from the physical interactions. And according to the argument based on the macromolecular confinement, an increase in νcov 0 increases ∆G because the confined space favors the formation of the binding. This, in effect, enhances the contribution from physical interactions to the overall shear moduli. We plan to confirm the second argument in future studies. Hellio-Serughetti et al. used gelatin gels crosslinked by bisvinylsulfonemethyl and observed that the addition of the covalent crosslinker enhanced the contribution of the physical crosslinks to the shear moduli, which is similar to the findings shown here.55 The authors attributed it to the altered secondary structure and rigidity of the triple helices formed by gelatin, caused by the addition of covalent crosslinks. However, the physical crosslinking of their work was driven by the hydrogen bonding whereas the physical crosslinking in this article was ionic in nature. In addition, the contribution of the secondary structure of the physical crosslinks may not be significant in our work since relatively short peptides were used. Therefore,

it is not certain whether their explanation would apply to the present work. However, it is possible that the addition of the covalent crosslinker to the gelatin gel may have caused molecular confinement thereby enhancing the physical interactions between gelatin triple helices. ECM resembles the described hydrogel in that it is composed of numerous covalent and physical interactions. Physical interactions include the interactions between polysaccharides, polysaccharide and protein and protein and protein. Collagen binds to other collagen molecules through hydrogen bonding to form triple helical collagen fibers.56 Glycosaminoglycans (GAGs) are known to bind physically to each other and to collagen fibers and form bridges between the collagen fibers. These physical interactions are known to play important roles in dissipating the mechanical loads on the tissues.57 Because these interactions take place within dense macromolecules connected through various covalent and physical networks, it is possible that the ECM may possess similar viscoelastic properties as the hydrogel presented in this paper. One potential implication of the results of this paper is the effect of temperature on the mechanical properties of the ECM, which has not received much attention. Even though human body is maintained at a constant temperature, certain parts of the body, such as skin, experience mild temperature changes. Temperature changes can also occur inside the body in some special situations such as inflammation.58 Various therapies involve mild local temperature changes as well.59 As was presented in the results, the local temperature changes may alter the mechanical properties of the ECM significantly because the physical bonds between the molecules are formed within the covalent matrix. Chae et al. showed that the stiffness of cartilage was greatly reduced at high temperatures (40∼75 °C),60 which is consistent with our results except for the temperature range that was used. Because many cellular activities including cell migration, cell adhesion, and cell proliferation have been found to be affected by the mechanical properties of the ECM, and the local temperature changes, in turn, can alter the mechanical properties of the ECM, the local temperature changes should have great influence on many cellular functions. For instance, one of the outcomes of inflammation is the increase of local temperature. Even though the leukocyte migration is known to be guided by the chemokines, the local gradient of ECM mechanical properties caused by the local temperature gradient may participate in guiding the leukocytes. The hydrogel presented in this paper can serve as a model system to understand how the temperature affects cellular functions such as cell migration. One of the potential problems of this hydrogel system is that most of the heparin-peptide interactions melted at relatively low temperatures and its mechanical properties did not change significantly around the physiologically relevant temperatures. Identifying the peptide sequences with higher affinities toward heparin will make the system more relevant and useful for future cell studies.

V. Conclusion Multiarm PEG-based hydrogels with various ratios of physical and covalent crosslinks were characterized with rheometry to understand how both physical and covalent bonds affect the mechanical properties of the gel. It was found that the physical and covalent bonds within the hydrogel are not independent but influence the overall mechanical properties of the gel in a complex fashion. Specifically, the characteristics of the physical bonds became more pronounced when the covalent crosslinks were added to the hydrogel resulting in a much stiffer gel that


responded more sensitively to the environmental changes. This effect was explained in terms of the stress relaxation times of the polymer. The purely physical system, which was made of small clusters, relaxed too quickly to resist the external stress. Therefore, the physical bonds could not contribute significantly to the overall shear moduli. On the other hand, when covalent crosslinkers were added, stress relaxation time of the hydrogel increased. In this condition, the physical bonds that form at any time can contribute to the overall moduli. In addition to the increased conformational stress relaxation time, the macromolecular confinement, which can shift the equilibrium significantly toward more compact molecular conformations, may be responsible for the striking difference in the viscoelastic properties of the gels. Kd measurements by QCM indicated that the enhanced mechanical properties of the hydrogel in the presence of the covalent crosslinks are partially due to the increased binding affinity between heparin and peptide within the dense covalent network. These results may have implications in many biological processes which involve local temperature changes such as in inflammation because the local temperature changes can alter the mechanical properties of the ECM, which in turn can affect various cellular activities such as cell migration and adhesion. We believe that this hydrogel can serve as a model system to understand the relationships between the temperature and the mechanical properties of the ECM and the cell functions. Acknowledgment. This work was funded by the National Science Foundation CAREER: CBET 0651643.

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BM801270K

Interplay between Covalent and Physical Interactions within

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